Vista thinks Wireless receiver is on when it's off

The laptop has Wi-fi capabilities, and there is a button to turn this off and on, with a corresponding LED to notify you. Also, when you press the button, you get a Windows pop-up box that says "Wireless LAN Wi-fi" with a check-box next to it. Pressing the button toggles the check-box off and on.

The issue I am having is that even if my wireless capability is supposed to be off (with the LED not lit and the box unchecked), Windows Vista can still connect to my home wireless network and I am still able to go on the internet!

I have had a look at these laptops and your wirless card seems very popular in them. There are a number of reported issues and fixes for drivers for Vista but nothing like your problem most seem to be around getting the card to work or configured. I would guess at a driver issue but unless this is really driving you mad I would leave well alone while the wifi is working.